It would probably take a billion dollars to develop and market a new OS. That still wouldn't guarantee any significant market share even if the price were $1 per installation. It would probably take another billion or at least several hundred million to get a lot of great applications ported to it without said marketshare.

They could do it, but it would likely be more of a bespoke/vanity sort of thing. I don't know if they could really make it fly for the masses.

They'd likely have a better chance of creating a site to compete with eBay. And I don't think that could be done even by a Google-Microsoft-Amazon-Yahoo consortium.